Besides the two procedures specially designed for the changepoint detection problem in exponential families, detecting changes in the characteristics of a sequence of observed random variables has a long history and experienced a renaissance in recent years boosted by a flourishing development in bioinformatics (e.g. [1]}, [2]}, [3]}, [4]} and [5]}). It also has attracted attention from other fields including climatology (e.g. [6]} and [7]}), financial econometrics (e.g. [8]}) and signal processing (e.g. [9]} and [10]}), among many others. Within the regime of univariate mean changepoint detection, theoretical analysis has been established recently by [11]} and [12]}.
A recently selective review of the related literature can be found in [13]}. We only mention some representative procedures here. [14]} proposed a binary segmentation (BS for short) method to detect the changes in means. A modified procedure circular binary segmentation (CBS for short) was provided by [1]} then a faster algorithm was given in [16]} which has achieved a big success in genome analysis. Later, to enhance the robustness to departures from standard model assumptions, another method (denoted as cumSeg in the sequel) had been tailor-made by [5]} to detect changes in genomic sequences. In the direction of reducing the complexity of computation, the pruned exact linear time (PELT for short) method was proposed by [18]} where they also showed PELT leads to a substantially more accurate result than BS. Wild binary segmentation (WBS for short) is an approach proposed by [19]} based on a development of BS and it becomes quite popular nowadays due to its nice performance and an easy implementation. Aimed at improving SMUCE ([20]}) especially under the situation with low signal-to-noise ratio or with many changepoints compared to the length of observations, [21]} proposed an alternative multiscale segmentation method (denoted as FDR in the sequel) by controlling the false discovery rate of their whole segmentation procedure. In the direction of being robust in the presence of outliers, [22]} proposed an algorithm (denoted as robseg in the sequel) based on the idea of adapting existing penalized cost methods to some loss functions which are less sensitive to the outliers. Two examples of the loss functions to which their procedure applies are the Huber loss and biweight loss. In practice, based on the same observations, different approaches mentioned above may give different estimators. As it was point out by the comparison study in [23]}, it is rather rare that one particular method uniformly outperforms another. Given so many experts' suggestions, a realistic and also interesting question is which one we should pick? Or in another word, can we let the data decide the preference of several (possibly random) estimators case by case so that finally we can always achieve a nearly optimal performance among the candidates taken into consideration?
